Jeb Bush, the former Florida governor and brother of the ex-president, has warned Mitt Romney that he has boxed himself in politically with rhetoric over illegal immigration and said Republicans need a change of tone on the issue if they are to win over Latino voters.

Bush said that immigration was among issues that have seen Republicans become so partisan that even Ronald Reagan would face trouble winning the party's presidential nomination today because he co-operated with Democrats.

The former governor, who has been touted as a possible running mate for Romney but who says he does not want the job, told a meeting with Bloomberg journalists that Romney needs to break away from talking about immigration solely in the context of undocumented aliens and tightening borders.

"Don't just talk about Hispanics and say immediately we must have controlled borders," he said. "It's kind of insulting when you think about it. Change the tone would be the first thing. Second, on immigration, I think we need to have a broader approach."

Florida is a key battleground in November's presidential election. Obama won two-thirds of the Hispanic vote there 2008.

Bush said Romney had understandably zeroed in on illegal immigration during the Republican primaries, talking about tightening border controls and other measures in order to connect with voters who accuse undocumented aliens of taking jobs and burdening the health and education systems. But the former governor said that in doing so, Romney had alienated other voters.

"Governor Romney has used this as a means to contact with a group of voters who were quite angry … so he's in somewhat of a box," he said. "The broader question is how you get out of it."

Bush said Romney had "work to do" to win over Latinos. "I think he needs to campaign in Hispanic communities, which he's doing. I think he needs to broaden the issue out, to make it an economics issue as much as it is a rule of law … Have a broader message and have a more intense message. There is work to do, though," he said. "I'd say that, if an objective teacher was grading where we are right now, I'd say 'needs improvement' – hopefully not an unfinished grade."

But Bush admitted his is not the prevailing view among Republicans, many of whom support measures such as the Arizona law, now the subject of a supreme court challenge, requiring police to check the immigration status of people they stop and making it a criminal offence to be in the state as an illegal immigrant.

"I do feel a little out of step with my party on this," he said.

The former governor also said that the Republican party has become so partisan that today Reagan "would be criticised for doing the things that he did".

Many on the right of the Republican party, particularly those allied with the Tea Party movement, see compromise and co-operation with the Democrats as tantamount to surrender. Bush described the partisanship as "disturbing".

"Ronald Reagan would have, based on his record of finding accommodation, finding some degree of common ground, similar to my dad [George Bush senior], they would have a hard time if you define the Republican party, and I don't, as having an orthodoxy that doesn't allow for disagreement, doesn't allow for finding some common ground," he said. "Back to my dad's time and Ronald Reagan's time – they got a lot of stuff done with a lot of bipartisan support but right now it's just difficult to imagine."

Bush pointed to the budget deal his father agreed with the Democratic party leadership in Congress which he said bolstered the economy but cost his father re-election because it angered conservatives by requiring him to break a pledge that there would be no new taxes.

"Politically it clearly didn't work out. He was a one-term president," said Bush.But Bush also blamed Barack Obama for widening the political divide and said both parties have contributed to "this dysfunction".

"His first year could have been a year of enormous accomplishment had he focused on things where there was more common ground," he said in reference to co-operation on spending and public debt.

Asked about potential running mates for Romney, Bush praised a Florida senator, Marco Rubio, saying that he was more experienced than Obama at this stage in his career. ''He would bring energy to a campaign that could always use it. He's the real deal," he said.